The van der Waals interactions (vdW) between the π-conjugated molecules offer new opportunities for fabricating the heterojunction-based devices and investigating charge transport in heterojunctions with atomic thickness. In this work, we fabricate sandwiched single-molecule bilayer-graphene junctions via vdW interactions and characterize their electrical transport properties by employing the cross-plane break junction (XPBJ) technique. Experimental results show that the cross-plane charge transport through single-molecule junctions is determined by the size and layer number of molecular graphene in these junctions. Density functional theory (DFT) calculations reveal that the charge transport through the molecular graphene in these molecular junctions is sensitive to the angles between the graphene flake and peripheral mesityl groups, and those rotated groups can be used to tune the electrical conductance. This study provides new insight into cross-plane charge transport in atomically thin junctions and highlights the role of through-space interactions in vdW heterojunctions at the molecular scale.